Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
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Comparison with least-squares solution<br />
histograms of residuals Ax−b, with randomly generated A ∈ R 200×80 , for<br />
10<br />
8<br />
6<br />
4<br />
2<br />
01.5<br />
100<br />
80<br />
60<br />
40<br />
20<br />
¡1.5 0<br />
x ls = argmin‖Ax−b‖, x l1 = argmin‖Ax−b‖ 1<br />
1.0<br />
0.5 0.0 0.5 1.0 1.5<br />
(Ax ls −b) k<br />
¡¡1.0<br />
0.5 0.0 0.5 1.0 1.5<br />
(Ax l1 −b) k<br />
l 1 -norm distribution is wider with a high peak at zero<br />
<strong>Piecewise</strong>-<strong>linear</strong> <strong>optimization</strong> 2–11
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